A nine-point scheme with explicit weights for diffusion equations on distorted meshes
A nine-point scheme with explicit weights for diffusion equations on distorted meshes
复制标题
扭曲网格上扩散方程的具有显式权重的九点方案
DOI：
10.1016/j.apnum.2011.01.012
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发表时间：
2011-07
影响因子：
2.8
通讯作者：
Gao Zhiming
中科院分区：
文献类型：
--
作者：
Wu Jiming;Gao Zhiming
本文针对结构化四边形网格，导出了一种九点差分格式，该格式具有五个中心元和四个顶点元。顶点未知数被视为中间的，并表示为一个线性组合的相邻的细胞为中心的未知数，这减少了该计划的一个细胞为中心的一个与一个本地模板涉及9个细胞为中心的未知数。线性组合中的系数被称为权重，并提出了两种新的权重。这些新的权值既不依赖于网格的不连续性，也不依赖于网格的拓扑结构，具有显式的表达式，可以简化为非均匀矩形网格上的一维调和平均权值，而且易于推广到非结构化多边形网格和非匹配网格上.九点格式的推导和新权的推导都满足线性保持准则。数值实验表明，采用这些新的权系数，九点差分格式及其简单扩展格式在包括结构化四边形网格、非结构化多边形网格和非匹配网格在内的许多高畸变网格上都具有接近二阶的精度.
In this paper, for the structured quadrilateral mesh we derive a nine-point difference scheme which has five cell-centered unknowns and four vertex unknowns. The vertex unknowns are treated as intermediate ones and are expressed as a linear combination of the neighboring cell-centered unknowns, which reduces the scheme to a cell-centered one with a local stencil involving nine cell-centered unknowns. The coefficients in the linear combination are known as the weights and two types of new weights are proposed. These new weights are neither discontinuity dependent nor mesh topology dependent, have explicit expressions, can reduce to the one-dimensional harmonic-average weights on the nonuniform rectangular meshes, and moreover, are easily extended to the unstructured polygonal meshes and non-matching meshes. Both the derivation of the nine-point scheme and that of new weights satisfy the linearity preserving criterion. Numerical experiments show that, with these new weights, the nine-point difference scheme and its simple extension have a nearly second order accuracy on many highly distorted meshes, including structured quadrilateral meshes, unstructured polygonal meshes and non-matching meshes.
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DOI：
10.1016/j.jcp.2008.11.031
发表时间：
2009-04
期刊：
J. Comput. Phys.
影响因子：
--
作者：
M. Basko;J. Maruhn;A. Tauschwitz
通讯作者：
M. Basko;J. Maruhn;A. Tauschwitz
DOI：
10.1051/m2an:2005047
发表时间：
2005-11
期刊：
Mathematical Modelling and Numerical Analysis
影响因子：
--
作者：
K. Domelevo;P. Omnes
通讯作者：
K. Domelevo;P. Omnes
DOI：
10.1137/050638473
发表时间：
2006-09
期刊：
SIAM J. Numer. Anal.
影响因子：
--
作者：
M. Wheeler;I. Yotov
通讯作者：
M. Wheeler;I. Yotov
DOI：
10.1016/j.jcp.2007.09.021
发表时间：
2008
期刊：
J. Comput. Phys.
影响因子：
--
作者：
Qian-Yong Chen;J. Wan;Yahan Yang-;R. Mifflin
通讯作者：
Qian-Yong Chen;J. Wan;Yahan Yang-;R. Mifflin
影响因子：
4.4
作者：
A. Poynter
通讯作者：
A. Poynter